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2 years ago

12

Factored completely, the expression 3x^2 - 3x - 18 is equivalent to

1 answer:

Dima020 [189]2 years ago

4 0

Answer:

3(x−3)(x+2)

Step-by-step explanation:

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A box of volume 180 m3 with square bottom and no top is constructed out of two different materials. The cost of the bottom is $4

zysi [14]

Answer:

Side of square bottom=6.46 m

Height of box=4.31 m

Step-by-step explanation:

Let s be the side bottom

Height of box=h

Volume of box= $180m^3$

Volume of box= $lbh=s^2h$

$s^2h=180$

$h=\frac{180}{s^2}$

Cost of bottom=$40 per square m

Cost of sides =$30 per square m

Total cost= $C=40s^2+30(4sh)$

$C=40s^2+120s\times \frac{180}{s^2}$

$C(s)=40s^2+\frac{21600}{s}$

Differentiate w.r.t s

$C'(s)=80s-\frac{21600}{s^2}$

$C'(s)=0$

$80s-\frac{21600}{s^2}=0$

$80s=\frac{21600}{s^2}$

$s^3=\frac{21600}{80}=270$

$s=(270)^{\frac{1}{3}}=6.46$

Again,differentiate w.r.t s

$C''(s)=80+\frac{43200}{s^3}$

Substitute s=6.46

$C''(6.46)=80+\frac{43200}{(6.46)^3}=240.2>0$

Hence, the cost is minimum at s=6.46

$h=\frac{180}{s^2}=\frac{180}{(6.46)^2}=4.31$

Side of square bottom=6.46 m

Height of box=4.31 m

5 0

2 years ago

Laws of exponents:<br>Squares and Square roots:<br><br>√9a¹⁶b³⁶

Nadusha1986 [10]

Step-by-step explanation:

Square root is equivalent to 1/2 power:

${(9 {a}^{16} {b}^{36} )}^{ \frac{1}{2} }$

Square root of 9 is 3. Multiply the exponents by 1/2 to get:

$3{a}^{8} {b}^{18}$

8 0

2 years ago

Ket [755]

First off, nicely done on the exponents. You'd be surprised on how bad some look ,:D

a)
$(3xy^{3})(2x^{2}y)\\ (3*2)(x*x^{2})(y^{3}*y)\\\\ 6x^{3}y^{4}$

b)
$2y(2y+3y^{2})-y^{2}(3-y)\\ (4y^{2}+6y^{3}) + (-3y^{2}+y^{3})\\ (6y^{3}+y^{3})+(4y^{2}-3y^{2})\\ 7y^{3}+y^{2}\\\\ y^{2}(7y+1)$

8 0

3 years ago

- To make homemade window cleaner, Shivani combines vinegar and water in the ratio of 1:7 by volume. How

rewona [7]

V:W
1:7
1+7=8
1/8*45=5.625 ml of vinegar

8 0

2 years ago

What must be true in order for line A to be parallel of line b?

AysviL [449]

Answer:

Its the first option.

Step-by-step explanation:

if they are both 180° then they can both go on forever without touching each other.

5 0

3 years ago

Read 2 more answers